The actor wrote two songs for the new release with musician Jeff Beck, who he appeared on stage with during his defamation trial against ex-wife Heard.
In a review of the record by The Sunday Times, lyrics from the album are revealed, one of which sees Depp sing: “I think you’ve said enough for one motherf***ing night.”
On another track, this one titled “Sad Motherf***ing Parade”, Depp says: “You’re sitting there like a dog with a seven-year itch,” adding: “If I had a dime, it wouldn’t reach your hand.”
The album, titled 18, will be released on Friday (15 July). Depp’s songs are the only two original songs on the record, with the remainder of the tracklist made up of covers of songs by Lou Reed, The Velvet Underground and The Beach Boys.
Depp won the highly publicised trial against Heard, with a jury finding that Heard had defamed the Pirates of the Caribbean actor on all three counts. He was awarded $10m (£8m) in compensatory damages and $5m (£4m) in punitive damages.
Meanwhile, Heard was awarded $2m (£1.6m) in compensatory damages, but no punitive damages.
In the wake of the verdict, Heard’s attorney appeared on morning talk shows to say that her client would be unable to pay the $8.35m (£6.65m) in damages to Depp.
Depp was recently forced to issue a warning to his fans in regards to his social media presence following a rise in fake accounts.